14%20-%20Indefinite%20Integration

14%20-%20Indefinite%20Integration - PROBLEMS 14 -...

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Unformatted text preview: PROBLEMS 14 - INDEFINITE INTEGRATION Page 1 ( Answers at the end of all problems ) Integrate the following functions with respect to x: ( 1 ) 1 1 x x x 2 2 4 + + + ( 2 ) 1 x 2 x 2 6 + + ( 3 ) 1 x x 2 4 + ( 4 ) 2 1 2 2 2 1 x log- − ( 5 ) x sin- 1 x sin ( 6 ) 1 e 1 e x x 2 2- + ( 7 ) x sin x cos 1 2 2 ( 8 ) x sin b x cos a 1 2 2 2 2 + ( 9 ) x tan 1 1 + ( 10 ) 3 x 1 x 1- ( 11 ) 1 x 1 x 4 2- + ( 12 ) x cos 4 x sin 3 x cos x sin 2 2- ( 13 ) ) x 2 ( 2x cos 1 π π < < + / ( 14 ) 4 x 1 x tan x 2 1- + ( 15 ) ) x ( x sin 1 x sin π < < + ( 16 ) ) 4 x 4 ( 2x sin 1-- / / π π < < ( 17 ) x 2 sin x sin ( 18 ) cot 6 x ( 19 ) x sin x cos 2 3 ( 20 ) ) b x ( sin ) a x ( sin 1-- ( 21 ) x cos x sin 4 2 ( 22 ) 3 x 1 x- ( 23 ) x sin 3 + x cos 4 + 5 1 ( 24 ) 3 1 2 1 x x 1- ( 25 ) x 1 1 x- + ( 26 ) )- x ( x cos 1 x cos π < < ( 27 ) x x 5- ( 28 ) 2 1 2 3 ) 2 x ( ) 1 x ( 1-- ( 29 ) sin 2 x cos 2x ( 30 ) 1 x 2x 1 x 3 2 + + + PROBLEMS 14 - INDEFINITE INTEGRATION Page 2 ( Answers at the end of all problems ) ( 31 ) 4 a x x 1- 4 ( 32 ) ) x 4 ( ) 1 x ( 1-- ( 33 ) 2 2 x x 25- ( 34 ) ) 2a x ( x 2ax x 1 2- < < ( 35 ) cos x sin 2 2x ( 36 ) 2 x 2x 8 1 x 3-- + ( 37 ) x 2 e 3x ( 38 ) ) 2 x ( ) 1 3x (- + ( 39 ) 5 x e 2x - 1 ( 40 ) 1 x x 4 2 + ( 41 ) x sinx cos 3x ( 42 ) 2 x 2ax x- ( 43 ) 2 1 x 1 x sin- + ( 44 ) 1 x x 1- + ( 45 ) ) x ( x 1 x 1 cos 2 2 1-- < + ( 46 ) 2 9 2 3 ) x 1 ( x + ( 47 ) ) a 0, x ( ) a x ( x 2 3 2 2 2- > > ( 48 ) x 2 2 e ) 1 x ( 1 x + + ( 49 ) x sin 5x sin ( 50 ) x tan x 1 2- ( 51 ) x sin 2 x ( 52 ) x sec 2 x tan x ( 53 ) 2x sin e 2 x- ( 54 ) 1 x 1- 4 ( 55 ) 2 x cos 2 x ( 56 ) sec 4 x ( 57 ) ) 4 x ( ) 1 x ( x 3 3 2- + ( 58 ) e 2x sin 3x sin x ( 59 ) sec 3 x ( 60 ) ) 2 x ( ) 2 3x ( x- 2 + PROBLEMS 14 - INDEFINITE INTEGRATION Page 3 ( Answers at the end of all problems ) ( 61 ) ) 5 x ( ) 2 x ( x 2 2 3 + + ( 62 ) 1 5e 6e 1 x 2x + + ( 63 ) ) 4 x ( ) 1 x ( 1 2- + ( 64 ) x sin x cos x sin x cos 1 1 1 1----- + ( 65 ) x cos x sin ( 66 ) x 2 cos ( log x ) ( 67 ) ) b x ( ) a x ( x 2 2 2 2 + + ( 68 ) x x 1 4x x-- 3 2 + ( 69 ) 2) x ( 1) x ( x 2 2 2 + + ( 70 ) ) 2 x ( e x cos 1 x sin 1-- 2 x / < < + π ( 71 ) ) 1 x ( x 1 3 + ( 72 ) x 4 sin x sin ( 73 ) ) x sin 2 1 ( x cos 1 + ( 74 ) 2x sin x sin 1 + ( 75 ) x tan ( 76 ) x a x- ( 77 ) 1 x x 1 x x 2 2 4 + + + + ( 78 ) x 1 ) x 1 (- + ( 79 ) sin x cos x ( sin 2x + cos 2x ) ( 80 ) 2x sin x cos x sin + ( 81 ) 2 2 2 2 x a x a x- + ( 82 ) x tan 4 3 x tan 2 + ( 83 ) 2 3 2x x ) e e ( 1- + ( 84 ) 3 4x ) 1 x 2 ( 1 + + ( 85 ) 2 2 x 1 x 1- + ( 86 ) 2 x 1 ) x 1 ( 1- + ( 87 ) x sin 3 2x cos 1 2 + ( 88 ) ) 4 x ( ) 5 x ( 7 x 6-- + ( 89 ) sin 4 3x cos 2...
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This note was uploaded on 11/28/2011 for the course PHYSICS 300 taught by Professor Smith during the Spring '06 term at ITT Tech Flint.

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14%20-%20Indefinite%20Integration - PROBLEMS 14 -...

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